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In another letter to two unnamed friends :
I have been challenged by two patriots - it was impos-
sible for me to refuse. I beg your pardon for having advised
neither of you. But my opponents had put me on my
honour not to warn any patriot. Your task is very simple:
prove that I fought in spite of myself, that is to say after
having exhausted every means of accommodation. ...
Preserve my memory since fate has not given me life
enough for my country to know my name. I die your friend
These were the last words he wrote. All night, before writing
these letters, he had spent the fleeting hours feverishly dashing
off his scientific last will and testament, writing against time to
glean a few of the great things hi his teeming mind before the
death which he foresaw could overtake him. Tune after tune he
broke off to scribble in the margin ;I have not time; I have not
time,' and passed on to the next frantically scrawled outline.
What he wrote hi those desperate last hours before the dawn
will keep generations of mathematicians busy for hundreds of
years. He had found, once and for all, the true solution of a
riddle which had tormented mathematicians for centuries:
under what conditions can an equation be solved? But this was
only one thing of many. In this great work, Galois used the
theory of groups (see chapter on Cauchy) with brilliant success.
Galois was indeed one of the great pioneers hi this abstract
theory, to-day of fundamental importance in all mathematics.
In addition to this distracted letter Galois entrusted his
scientific executor with some of the manuscripts which had
been intended for the Academy of Sciences. Fourteen years
later, in 1'846, Joseph Liouville edited some of the manuscripts
for the Journal de Mathematiques pures et appliquees. Liouville,
himself a distinguished and original mathematician, and editor
of the great Journal, writes as follows in his introduction:
The principal work of Evariste Galois has as its object the
conditions of solvability of equations by radicals. The author
lays the foundations of a general theory which he applies in
detail to equations whose degree is a prune number. At the age of